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# Development of large scale tight-binding methods, and application to electron transfer in symmetric dielectric barrier discharges (DBDS)

#### Ghale, Purnima

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https://hdl.handle.net/2142/107878

## Description

- Title
- Development of large scale tight-binding methods, and application to electron transfer in symmetric dielectric barrier discharges (DBDS)
- Author(s)
- Ghale, Purnima
- Issue Date
- 2020-05-05
- Director of Research (if dissertation) or Advisor (if thesis)
- Johnson, Harley T
- Doctoral Committee Chair(s)
- Johnson, Harley T
- Committee Member(s)
- Ertekin, Elif
- Schleife, Andre
- Stephani, Kelly

- Department of Study
- Mechanical Sci & Engineering
- Discipline
- Mechanical Engineering
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Keyword(s)
- tightbinding
- electronic structure
- Landau-Zener dynamics
- time-dependence under AC voltage
- device physics, dielectric barrier discharges
- graph theory
- asynchronous programming
- density matrix calculations
- hysteresis

- Abstract
- Extending the size of electronic structure simulations is an ongoing effort at various levels of electronic structure theory. In tight-binding and density functional theory, the most expensive part of the computation is obtaining the density matrix, which traditionally scales cubically with the number of atoms. Tight-binding is a semi-empirical electronic structure method that is the least expensive among methods capable of resolving charge, energies and electronic wavefunctions at the atomistic level. While linearly scaling algorithms have been developed previously, the focus was on using localization or sparsity of the density matrix to obtain linear scaling. The disadvantage of this approach is that localization and sparsity are dependent on the basis-set choice, which is generally unknown apriori. Furthermore, calculations often also rely on matrix-matrix multiplication, which are harder to optimize over distributed nodes. Thus, we present a linearly scaling method that relies on sampling the density matrix via matrix-vector multiplication, by combining polynomial expansion and polynomial purification methods that are well-known in the tight-binding literature, allowing us to simulate multi-million atom systems on a large memory node on the campus cluster, as well as demonstrations of larger systems and faster, more accurate, simulations on the BlueWaters supercomputer. Next, we investigate the underlying microscopic mechanism for electron transfer in symmetric dielectric barrier discharge plasma generators (DBDs). DBDs are useful in a wide variety of applications where the plasma generated is used for materials processing, combustion, and flow control. Our interest is in determining the rate of electron emission from dielectrics under AC voltage. While phenomenological models have existed, a microscopic electronic-structure based model to compute and predict the rate of electron transfer from dielectric surfaces had not been presented so far. We propose that electron transfer between the dielectric and gaseous regions under AC voltage, is a particular case of the Landau-Zener avoided level-crossing model, where electron transfer occurs between localized states due to time-dependent resonance. We first show that the temporal profile of current-voltage obtained from this model are consistent with experimental observations, and then go on to numerically compute the rates of electron transfer under a parametric sweep of AC voltages and frequencies. The dataset produced will be useful as boundary conditions in numerical plasma simulations as DBD devices are miniaturized and surface effects become more important -- previously, these values were experimentally inferred after plasma generation. Finally, motivated by the numerical results obtained from simulations of electron transfer within DBDs, we investigate how rate-dependent charge-voltage hysteresis might occur in closed finite systems driven at finite frequencies. While a lot of work has been done to characterize dissipation due to coupling to a bath, here we investigate how coherent unitary quantum dynamics give rise to dissipation and rate-dependent hysteresis in finite systems. We show irreversibility of closed quantum mechanical systems under finite driving near an avoided level-crossing, accompanied by representative simulations of spin-magnetic field hysteresis in spin-systems, charge-voltage hysteresis in a 50-atom finite flake of graphene, and charge-voltage hysteresis in a dielectric-gas-dielectric system driven at an AC frequency of 20 MHz.
- Graduation Semester
- 2020-05
- Type of Resource
- Thesis
- Permalink
- http://hdl.handle.net/2142/107878
- Copyright and License Information
- Copyright 2020 Purnima Ghale

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